This is an announcement for the paper "Characterization of compact subsets of $\mathcal{A}^p$ with respect to weak topology" by Hirbod Assa.
Abstract: In this brief article we characterize the relatively compact subsets of $\mathcal{A}^p$ for the topology $\sigma(\mathcal{A}^p,\mathcal{R}^q)$ (see below), by the weak compact subsets of $L^p$ . The spaces $\mathcal{R}^q$ endowed with the weak topology induced by $\mathcal{A}^p$, was recently employed to create the convex risk theory of random processes. The weak compact sets of $\mathcal{A}^p$ are important to characterize the so-called Lebesgue property of convex risk measures, to give a complete description of the Makcey topology on $\mathcal{R}^q$ and for their use in the optimization theory.
Archive classification: math.PR math.FA
Remarks: 8 pages
The source file(s), compactsetsAssa.H.tex: 19008 bytes, is(are) stored in gzipped form as 0804.2873.gz with size 6kb. The corresponding postcript file has gzipped size 67kb.
Submitted from: assa@dms.umontreal.ca
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